NEW YORK — Few people get to meet a U.S. president. Dule Hill has met four — one fake and three real ones. And now he’s gotten to strut his stuff in front of a sitting one.

The actor and dancer, who played a personal presidential aide on “The West Wing,” got a chance to perform a song for hundreds of world leaders, including President Barack Obama, on Monday night during a reception for U.N. leaders.

Hill and cast members of the upcoming Broadway musical “After Midnight,” a musical celebrating Duke Ellington’s years at the famous Cotton Club nightclub in Harlem, sang a few numbers at the Waldorf Astoria, a swanky Park Avenue hotel. Hill sang “I’ve Got the World on a String,” and other cast members sang the songs “Devil and the Deep Blue Sea” and “Creole Love Call.”

“I really enjoyed it,” Hill said afterward. “I never thought this would ever happen. If you’d have told me I was going to sing in front of all these dignitaries a month ago I would have laughed.”

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It’s just Hill’s latest close encounter with a commander in chief: He met Jimmy Carter at a Democratic National Convention a few years ago and has met Bill Clinton many times, even watching his last State of the Union from the White House. And Hill was, of course, a close associate of Josiah Bartlet, the president played by Martin Sheen on “The West Wing.”

Hill learned only last Wednesday that he’d scored his latest gig. He had met Obama when he was a senator and running for the White House, but this meeting would be different.

“It’s not something that happens every day,” said Hill, who plays the master of ceremonies in the upcoming show. “When they asked me, it wasn’t like I said, ‘Well, let me check my schedule. I might want to watch the game.’”

“After Midnight,” directed and choreographed by Warren Carlyle with musical direction by Wynton Marsalis, appeared off-Broadway last year at New York City Center under the name “Cotton Club Parade.” Songs include “Stormy Weather” and “I Can’t Give You Anything But Love.”

Performances start Oct. 18 at the Brooks Atkinson Theatre, with an official opening night set for Nov. 3. Hill joins Grammy Award- and “American Idol” winner Fantasia Barrino in the lively show, which will feature 17 musicians and 25 vocalists and dancers.

Hill, who starring in USA’s hit detective series “Psych,” was last on Broadway as Spoon, a lawyer-turned-budding novelist, in Lydia R. Diamond’s thoughtful family drama “Stick Fly” in 2011.

Emmy Award-nominated for his work as Charlie Young on “The West Wing,” Hill first came to prominence as The Kid opposite Savion Glover and Jeffrey Wright in “Bring in ‘da Noise, Bring in ‘da Funk.”

The Obamas have been big boosters of Broadway. First lady Michelle Obama and daughters Sasha and Malia have attended performances of “Memphis,” “Spider-Man: Turn Off the Dark,” “Sister Act,” “The Trip to Bountiful,” “Motown the Musical” and “The Addams Family.” And the first couple saw “Joe Turner’s Come and Gone” during a date night in 2009. Michelle Obama and six girlfriends also saw “Fela!” in 2010.